On a generalized divisor problem II

Generalized divisor problem

In 1952 H.E. Richert by means of the theory of Exponents Pairs (developed by J.G. van der Korput and E. Phillips ) improved the above O-term ( see [8] or [4] pag. 221 ). In 1969 E. Krätzel studied the three-dimensional problem. Besides, M.Vogts (1981) and A. Ivić (1981) got some interesting results which generalize the work of P.G. Schmidt of 1968. In 1987 A.Ivić obtained Ω-results for ∫ T 1 ∆ ...

On the Riemann Zeta-function and the Divisor Problem Ii

Let ∆(x) denote the error term in the Dirichlet divisor problem, and E(T ) the error term in the asymptotic formula for the mean square of |ζ( 1 2 + it)|. If E∗(t) = E(t) − 2π∆∗(t/2π) with ∆∗(x) = −∆(x) + 2∆(2x) − 1 2 ∆(4x), then we obtain ∫ T 0 |E(t)| dt ≪ε T 2+ε and ∫ T 0 |E∗(t)| 544 75 dt ≪ε T 601 225 . It is also shown how bounds for moments of |E∗(t)| lead to bounds for moments of |ζ( 1 2 ...

On Dirichlet ' S Divisor Problem

tact, whereas those for a = 0.02 imply only 25% more frequent contacts than the all-ornone hypothesis but with rather high though rapidly diminishing attack rates. 10 Schuman and Doull, Amer. Jour. Pub. Health, 30, Supplement to March, 1940, p. 21, state: "From these estimates of carrier prevalence and froni the average annual increment in Shick-negatives, an estimate may be made of the number ...

Some Asymptotic Formulas on Generalized Divisor Functions

1 . Throughout this paper, we use the following notation : c•1 , c2 , . . ., X0 , X1 , . . . denote positive absolute constants. We denote the number of elements of the finite set S by BSI . We write ex =exp (x) . We denote the least prime factor of n by p(n) . We write pall n if pain but pa+1 f n . v(n) denotes the number of the distinct prime factors of n, while the number of all the prime fa...

Some Remarks on Elementary Divisor Rings II